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        <article data-uid="Usage.HiMech.Topo">
          <h1 id="kinematic-topology">Kinematic Topology</h1>

<p>The Kinematic Topology is composed of three elemental classes: <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a></strong>, <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Branch.html">Branch</a></strong> and <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a></strong>.</p>
<h2 id="basic-elements">Basic Elements</h2>
<h3 id="anchors-and-branches">Anchors and Branches</h3>
<p><strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a></strong> object contains a cartesian coordinate. It can be a mechanical component or a flag.</p>
<p><strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Branch.html">Branch</a></strong> object is a directional link between two <a class="xref" href="../../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a> objects. It contains the <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a></strong> object. The <a class="xref" href="../../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a> object contains a coordinate <strong>transformation matrix</strong>. As shown in the following sketch:</p>
<p><img src="chainLink.png" alt="Chain Structure"></p>
<h3 id="assembly-management">Assembly Management</h3>
<p><strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a></strong> (Assembly) provides organization and management of Anchors. An Assembly can contain both Anchors and other Assemblies. Key features include:</p>
<ul>
<li>Grouping related Anchors together</li>
<li>Managing coordinate transformations</li>
<li>Providing display and indexing functions</li>
<li>Supporting hierarchical structure</li>
</ul>
<h2 id="kinematic-chain-example">Kinematic Chain Example</h2>
<p>The following figure shows a kinematic chain of a non-orthogonal 5-axis machine tool:</p>
<p><img src="vmt.png" alt="VMT Structure"></p>
<p>Each <a class="xref" href="../../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a> represents a component:</p>
<ul>
<li>Axis components: X, Y, Z, B, C</li>
<li>Base components: O (base1), O* (base2)</li>
<li>Tool components: S (spindle), T (tool body), T* (tool flute)</li>
<li>Workpiece: W</li>
</ul>
<p>The relative transform between two Anchors is calculated by multiplying the transform matrices along the Branch. For example, the transform matrix from W to T is:</p>
<div class="math">
\[
M_{WT} = M_{CW}^{-1} \cdot M_{YC}^{-1} \cdot M_{OY}^{-1} \cdot M_{OO^*} \cdot M_{O^*X} \cdot M_{XZ} \cdot M_{ZB} \cdot M_{BS} \cdot M_{ST}
\]</div>
<p>This matrix can be obtained using <a class="xref" href="../../../../../api/Hi.Mech.Topo.Asmb.html#Hi_Mech_Topo_Asmb_GetMat4d_Hi_Mech_Topo_IGetAnchor_Hi_Mech_Topo_IGetAnchor_">GetMat4d(IGetAnchor, IGetAnchor)</a>.</p>

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